Mathematics Commons^™

Templates For Representable Matroids, Kevin Manuel Grace

LSU Doctoral Dissertations

The matroid structure theory of Geelen, Gerards, and Whittle has led to a hypothesis that a highly connected member of a minor-closed class of matroids representable over a finite field is a mild modification (known as a perturbation) of a frame matroid, the dual of a frame matroid, or a matroid representable over a proper subfield. They introduced the notion of a template to describe these perturbations in more detail. In this dissertation, we determine these templates for various classes and use them to prove results about representability, extremal functions, and excluded minors.

Chapter 1 gives a brief introduction …

Two Results In Drawing Graphs On Surfaces, Joshua E. Fallon

LSU Doctoral Dissertations

In this work we present results on crossing-critical graphs drawn on non-planar surfaces and results on edge-hamiltonicity of graphs on the Klein bottle. We first give an infinite family of graphs that are 2-crossing-critical on the projective plane. Using this result, we construct 2-crossing-critical graphs for each non-orientable surface. Next, we use 2-amalgamations to construct 2-crossing-critical graphs for each orientable surface other than the sphere. Finally, we contribute to the pursuit of characterizing 4-connected graphs that embed on the Klein bottle and fail to be edge-hamiltonian. We show that known 4-connected counterexamples to edge-hamiltonicity on the Klein bottle are hamiltonian …

Developing A Model To Predict Prevalence Of Compulsive Behavior In Individuals With Ocd, Lindsay D. Fields

USF Tampa Graduate Theses and Dissertations

The most common method of diagnosing Obsessive-Compulsive Disorder is the Yale-Brown Obsessive Compulsive Scale, which measures the severity of symptoms without regard to compulsions. However, this scale is limited to only considering the quantifiable time and energy lost to compulsions. Conversely, current systems of brain imaging arrest mobility and thus make it virtually impossible to observe compulsions at all, focusing instead on neurological responses to external stimuli. There is little research which merges both approaches, to consider the neuro-physiological effects of obsessions as well as the physical response through compulsions. As such, this research is focused on developing a model …

Recent Trends In The Frequency And Duration Of Global Floods, Nasser Najibi, Naresh Devineni

Publications and Research

Frequency and duration of floods are analyzed using the global flood database of the Dartmouth Flood Observatory (DFO) to explore evidence of trends during 1985–2015 at global and latitudinal scales. Three classes of flood duration (i.e., short: 1–7, moderate: 8–20, and long: 21 days and above) are also considered for this analysis. The nonparametric Mann–Kendall trend analysis is used to evaluate three hypotheses addressing potential monotonic trends in the frequency of flood, moments of duration, and frequency of specific flood duration types. We also evaluated if trends could be related to large-scale atmospheric teleconnections using a generalized linear model framework. …

Limit Behavior Of Mass Critical Hartree Minimization Problems With Steep Potential Wells, Yujin Guo, Yong Luo, Zhi-Qiang Wang

Mathematics and Statistics Faculty Publications

We consider minimizers of the following mass critical Hartree minimization problem: e_λ(N) ≔ inf{u∈H¹(ℝ^d),‖u‖²₂=N} E_λ(u), where d ≥ 3, λ > 0, and the Hartree energy functional E_λ(u) is defined by E_λ(u)≔∫_R^d|∇u(x)|²dx + λ∫_R^d g(x)u²(x)dx − 1/2∫_R^d∫_R^d {u²(x)u²(y)/|x−y|²} dxdy. Here the steep potential g(x) satisfies 0 = g(0) = inf_ℝ^dg(x) ≤ g(x) ≤ 1 and 1 …

Optimization Of The Estimation Of Initial Perturbations In Linear Differential Systems, A Kojametov

Karakalpak Scientific Journal

The article deals with constant coefficients of differential system, for this purpose the function of Lyapunova has been used.

Solution Of Systems Of Linear Algebraic Equations By Modified Methods Of Paired Gradients, A Otarov

Karakalpak Scientific Journal

The article deals with several modifications of the method of conjugate gradients for solving systems of linear algebraic equations are carried out in the article, and the application of some of them is illustrated with the solution of a given system of equations.

Solution Of Systems Of Linear Algebraic Equations By Modified Methods Of Paired Gradients, Amanbay Otarov

Karakalpak Scientific Journal

The article deals with several modifications of the method of conjugate gradients for solving systems of linear algebraic equations are carried out in the article, and the application of some of them is illustrated with the solution of a given system of equations.

Optimization Of The Estimation Of Initial Perturbations In Linear Differential Systems, A Kojametov

Karakalpak Scientific Journal

The article deals with constant coefficients of differential system, for this purpose the function of Lyapunova has been used.

Optimization Of The Estimation Of Initial Perturbations In Linear Differential Systems, A Kojametov

Karakalpak Scientific Journal

The article deals with constant coefficients of differential system, for this purpose the function of Lyapunova has been used.

Rudolf Laban's Dream: Re-Envisioning And Re-Scoring Ballet, Choreutics, And Simple Functional Movements With Vector Signs For Deflecting Diagonal Inclinations, Jeffrey Scott Longstaff

Journal of Movement Arts Literacy Archive (2013-2019)

Several methods of movement notation, forerunners of modern-day Labanotation/Kinetography were published by Rudolf Laban in his 1926 book Choreographie. One of these has been referred to as vector signs because they represent movement as orientations (slopes) of lines through space. This article begins by comparing Labanotation direction symbols with Laban's earlier vector signs by looking at differences when simple sequences are scored in both formats. Concepts of space within the vector signs are examined, particularly Laban's idea of deflecting inclinations where movements are categorized as mixtures of two fundamental contrasting spatial and dynamic tendencies: dimensional stability and diagonal mobility. This …

Elements Of Calculus 1, Nur Dean

Open Educational Resources

No abstract provided.

Computing Minimum Rainbow And Strong Rainbow Colorings Of Block Graphs, Melissa Karanen, Juho Lauri

Michigan Tech Publications, Part 1

A path in an edge-colored graph G is rainbow if no two edges of it are colored the same. The graph G is rainbow-connected if there is a rainbow path between every pair of vertices. If there is a rainbow shortest path between every pair of vertices, the graph G is strongly rainbow-connected. The minimum number of colors needed to make G rainbow-connected is known as the rainbow connection number of G, and is denoted by src(G). Similarly, the minimum number of colors needed to make G strongly rainbow-connected is known as the strong rainbow connection number of G, and …

Gamma-Realizability And Other Musings On Inverse Domination, John Asplund, Joe Chaffee, James M. Hammer Iii, Matt Noble

Theory & Applications of Graphs

We introduce and study γ-realizable sequences. For a finite, simple graph G containing no isolated vertices, I ⊆ V(G) is said to be an inverse dominating set if I dominates all of G and I is contained by the complement of some minimum dominating set D. Define a sequence of positive integers (x₁,…, x_n) to be γ-realizable if there exists a graph G having exactly n distinct minimum dominating sets D₁,… D_n where for each i ∈ {1,… n}, the minimum size of an inverse dominating set in V(G) …

Soft Computing Ideas Can Help Earthquake Geophysics, Solymar Ayala Cortez, Aaron A. Velasco, Vladik Kreinovich

Departmental Technical Reports (CS)

Earthquakes can be devastating, thus it is important to gain a good understanding of the corresponding geophysical processing. One of the challenges in geophysics is that we cannot directly measure the corresponding deep-earth quantities, we have to rely on expert knowledge, knowledge which often comes in terms of imprecise ("fuzzy") words from natural language. To formalize this knowledge, it is reasonable to use techniques that were specifically designed for such a formalization -- namely, fuzzy techniques, In this paper, we formulate the problem of optimally representing such knowledge. By solving the corresponding optimization problem, we conclude that the optimal representation …

Homomorphism Of Fuzzy Multigroups And Some Of Its Properties, P. A. Ejegwa

Applications and Applied Mathematics: An International Journal (AAM)

In a way, the notion of fuzzy multigroups is an application of fuzzy multisets to the theory of group. The concept of fuzzy multigroups is a new algebraic structure of uncertainty which generalizes fuzzy groups. Fuzzy multigroup is a multiset of X x [0; 1] satisfying some set of axioms, where X is a classical group. In this paper, we propose the concept of homomorphism in fuzzy multigroups context. Some homomorphic properties of fuzzy multigroups are explicated. Again, we show that the homomorphic image and homomorphic preimage of fuzzy multigroups are also fuzzy multigroups. Finally, we present some homomorphic properties …

An Accelerate Process For The Successive Approximations Method In The Case Of Monotonous Convergence, A. Laouar, I. Mous

Applications and Applied Mathematics: An International Journal (AAM)

We study an iterative process to accelerate the successive approximations method in a monotonous convergence framework. It consists in interrupting the sequence of the successive approximations method produced at the kth iteration and substituting it by a combination of the element of the sequence produced at the iterate k + 1 and an extrapolation vector. The latter uses a parameter which can be calculated mathematically. We illustrate numerically this process by studying a freeboundary problems class.

An Ishikawa-Type Iterative Algorithm For Solving A Generalized Variational Inclusion Problem Involving Difference Of Monotone Operators, Mohd Ishtyak, Rais Ahmad

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we study a generalized variational inclusion problem involving difference of monotone operators in Hilbert spaces. We established equivalence between the generalized variational inclusion problem and a fixed point problem. We establish an Ishikawa type iterative algorithm for solving a generalized variational inclusion problem involving difference of monotone operators, which is more general than Mann-type iterative algorithm. An existence result as well as a convergence result are proved separately. The problem of this paper is more general than many existing problems in the literature. Several special cases of generalized variational inclusion problem involving difference of monotone operators are …

Incomplete Generalized (P; Q; R)-Tribonacci Polynomials, Mark Shattuck, Elif Tan

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider an extension of the tribonacci polynomial, which we will refer to as the generalized (p; q; r)-tribonacci polynomial, denoted by T_n;m(x).We find an explicit formula for T_n;m(x)which we use to introduce the incomplete generalized (p; q; r)-tribonacci polynomials and derive several properties. An explicit formula for the generating function of the incomplete generalized polynomials is determined and a combinatorial interpretation is provided yielding further identities.

System Reliability Using Generalized Intuitionistic Fuzzy Rayleigh Lifetime Distribution, Ali Ebrahimnejad, Ezzatallah B. Jamkhaneh

Applications and Applied Mathematics: An International Journal (AAM)

Reliability analysis as one of the important research topics in engineering has been researched by a number of authors. Reliability in classical distributions is based on precise parameters. It is usually assumed that parameters of distributions are precise real numbers. However, in the real world, the data sometimes cannot be measured and recorded precisely. In this paper, the concept of fuzzy reliability is extended by the idea of generalized intuitionistic fuzzy reliability. We investigate the reliability characteristics of systems using Rayleigh lifetime distribution, in which the lifetime parameter is assumed to be generalized intuitionistic fuzzy number. Generalized intuitionistic fuzzy reliability, …

Hypergeometric Inequalities For Certain Unified Classes Of Multivalent Harmonic Functions, Vimlesh K. Gupta, Poonam Sharma

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider unified classes PH (m, A,B) H and Q_H (m, A,B) H of multivalent harmonic functions F = H +G∈H(m) . Some hypergeometric inequalities for the functions of the class H(m) defined by generalized hypergeometric functions to be in these unified classes and its sub classes TP_H (m, A,B) H and TQ_H (m, A,B) H , respectively, are obtained. Results, involving some integral operators are also given. Further, some special cases of the results are mentioned.

Graceful Colorings And Connection In Graphs, Alexis D. Byers

Dissertations

For a graph G of size m, a graceful labeling of G is an injective function f : V (G) → {0, 1, . . . , m} that gives rise to a bijective function f ¹ : E(G) → {1, 2, . . . , m} defined by f ¹(uv) = |f (u) − f (v)|. A graph is graceful if it has a graceful labeling. Over the years, a number of variations of graceful …

A New Approach To Solve Multi-Objective Transportation Problem, Lakhveer Kaur, Madhuchanda \ Rakshit, Sandeep Singh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a simple approach is proposed to obtain the best compromise solution of linear multiobjective transportation problem (MOTP). Using this approach, we get unique efficient solution. Because unique efficient extreme point obtained by proposed approach directly leads to compromise solution, which is preferred by decision maker. Also this approach is simple to use and less time consuming. For the application of proposed approach, numerical examples are considered from existing literature and are solved with proposed method.

Toroidal Embeddings And Desingularization, Leon Nguyen

Electronic Theses, Projects, and Dissertations

Algebraic geometry is the study of solutions in polynomial equations using objects and shapes. Differential geometry is based on surfaces, curves, and dimensions of shapes and applying calculus and algebra. Desingularizing the singularities of a variety plays an important role in research in algebraic and differential geometry. Toroidal Embedding is one of the tools used in desingularization. Therefore, Toroidal Embedding and desingularization will be the main focus of my project. In this paper, we first provide a brief introduction on Toroidal Embedding, then show an explicit construction on how to smooth a variety with singularity through Toroidal Embeddings.

Simple Groups, Progenitors, And Related Topics, Angelica Baccari

Electronic Theses, Projects, and Dissertations

The foundation of the work of this thesis is based around the involutory progenitor and the finite homomorphic images found therein. This process is developed by Robert T. Curtis and he defines it as 2^{*n} :N {pi w | pi in N, w} where 2^{*n} denotes a free product of n copies of the cyclic group of order 2 generated by involutions. We repeat this process with different control groups and a different array of possible relations to discover interesting groups, such as sporadic, linear, or unitary groups, to name a few. Predominantly this work was produced from transitive groups …

On B-Chromatic Number Of Prism Graph Families, Nadeem Ansari, R. S. Chandel, Rizwana Jamal

Applications and Applied Mathematics: An International Journal (AAM)

A b-coloring of graph 𝐺 is a proper 𝑘-coloring 𝐶 that verifies the following property: for every color class 𝑐𝑖, 1≤𝑖≤𝑘, there exists a vertex 𝑥𝑖, with color 𝑐𝑖, such that all the other colors in 𝐶 are utilized in 𝑥𝑖 neighbors. The b-chromatic number of a graph 𝐺, denoted by 𝜑(𝐺), is the largest integer 𝑘 such that 𝐺 may have a b-coloring by 𝑘 colors. In this paper we discuss the b-coloring of prism graph 𝑌𝑛, central graph of prism graph 𝐶(𝑌𝑛), middle graph of prism graph 𝑀(𝑌𝑛) and the total graph of prism graph 𝑇(𝑌𝑛) and we …

Space-Time Discretizations Using Constrained First-Order System Least Squares (Cfosls), Kirill Voronin, Chak Shing Lee, Martin Neumüller, Paulina Sepulveda, Panayot S. Vassilevski

Portland Institute for Computational Science Publications

This paper studies finite element discretizations for three types of time-dependent PDEs, namely heat equation, scalar conservation law and wave equation, which we reformulate as first order systems in a least-squares setting subject to a space-time conservation constraint (coming from the original PDE). Available piece- wise polynomial finite element spaces in (n + 1)-dimensions for functional spaces from the (n + 1)-dimensional de Rham sequence for n = 3, 4 are used for the implementation of the method. Computational results illustrating the error behavior, iteration counts and performance of block-diagonal and monolithic geometric multi- grid preconditioners are …

Simulating The Electrical Properties Of Random Carbon Nanotube Networks Using A Simple Model Based On Percolation Theory, Roberto Abril Valenzuela

Physics

Carbon nanotubes (CNTs) have been subject to extensive research towards their possible applications in the world of nanoelectronics. The interest in carbon nanotubes originates from their unique variety of properties useful in nanoelectronic devices. One key feature of carbon nanotubes is that the chiral angle at which they are rolled determines whether the tube is metallic or semiconducting. Of main interest to this project are devices containing a thin film of randomly arranged carbon nanotubes, known as carbon nanotube networks. The presence of semiconducting tubes in a CNT network can lead to a switching effect when the film is electro-statically …

The Bellringer Sequence: Investigating What And How Preservice Mathematics Teachers Learn Through Pedagogies Of Enactment, Mary A. Ochieng

Dissertations

This study examines preservice teacher learning through pedagogies of enactment—approaches to teacher education that allow preservice teachers to learn by doing what teachers do. Preservice teacher (PST) learning is examined through the implementation of the Bellringer Sequence (BRS), a pedagogy of enactment conceptualized in the study. The BRS is centered around bellringers—brief mathematical tasks implemented as students arrive for class. The BRS is a sequence of four activities centered on a bellringer: preparation (for teaching a bellringer) implementation (of the bellringer with peers), debriefing (discussing the implementation as colleagues), and written reflection (about the effectiveness of the bellringer).

Practice-based approaches …

Induced Graph Colorings, Ian Hart

Dissertations

An edge coloring of a nonempty graph G is an assignment of colors to the edges of G. In an unrestricted edge coloring, adjacent edges of G may be colored the same. If every two adjacent edges of G are colored differently, then this edge coloring is proper and the minimum number of colors in a proper edge coloring of G is the chromatic index χ^/(G) of G. A proper vertex coloring of a nontrivial graph G is an assignment of colors to the vertices of G such that every two adjacent vertices of …